Unit 2: Refraction and Lenses
Problem Set A
Overview:
Problem Set A targets your understanding of refraction and your ability to use two equations in order to analyze physical situations. The two equations are
where c = 3.0 x 10^{8} m/s (speed of light in a vacuum) v_{material} = speed of light in a specific material n_{material} = index of refraction value of that material |
where n_{1} = index of refraction value of material 1 (on one side of the boundary) n_{2} = index of refraction value of material 2 (on the opposite side of the boundary) _{1} = angle of refraction of material 1 (on one side of the boundary) _{2} = angle of refraction of material 2 (on the opposite side of the boundary) |
There are four common skills which you will have to implement on several occasions in order to solve these 15 problems. These skills are described below:
1) Measuring an angle of incidence or refraction if given a diagram (problems #1 and #8):
The angle of incidence value is the angle measure between the incident ray and the normal line. The normal line is an imaginary line drawn perpendicular to the boundary at the location where the incident ray strikes the boundary. The angle of refraction value is defined in a similar manner; it is the angle measure between the refracted ray and the normal line. Making these measurements simply involves the placement of a protractor along the boundary with its origin placed at the location where the light ray strikes the boundary.
2) Relating the light speed in a given material with the index of refraction of that material (problems #2-#6 and #12 and #15):
The speed of a light ray is dependent upon the medium through which it travels. Light travels relatively slowly in a more optically dense material and faster in less optically dense materials. The index of refraction value (n) provides a direct measure of the optical density of a material. It can be used to relate the speed of light in that material (v) to the speed of light in a vacuum (c = 3.0 x 10^{8} m/s). The speed of light equation is stated above; it can be used to relate light speed to index of refraction values.
3) The use of Snell's law equation to determine an unknown quantity (problems #6-#15):
A light ray will undergo refraction (a change in direction of its path) at a boundary between two materials whenever it approaches the boundary at an angle of incidence other than zero degrees. This refraction occurs in a rather predictable manner as expressed by the Snell's law equation. Knowing the index of refraction values of the two materials on opposite sides of the boundary and the angle of incidence allows one to make a calculation of the angle of refraction. In a similar manner, knowing the two angles which a light ray makes with the normal line for both sides of the boundary and knowing one of the index of refraction values of the two materials allows one to determine the second index of refraction value.
4) The ability to picture/diagram a refraction situation involving one or more boundaries and to trace the path of light through the material(s) (problems #7, #10, and #14):
Refraction of light is part of a broader study of physics known as geometric optics. Any study involving angle measures, normal lines, and/or parallel lines will demand an understanding of basic geometry. Crucial to the understanding of geometric principles is the ability to picture a situation and even represent by means of a diagram. Combining this ability with the results of Snell's law calculations allows one to trace the path of a light ray through a material to the next boundary which it encounters. Using an effective diagram, angle information at the second boundary can be determined and used in a subsequent Snell's law calculation.
Additional Readings/Study Aids:
The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in accomplishing the above tasks.
View Sample Problem Set.
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